I just wondered if an ISP could wipe a Routers settings.
I agree with comments above that the signs are almost certainly of a knackered router, but to take your ISP comment, the only one I know of - though there are doubtless others - is BT with the BT Home Hub.
The standard* software on a BT Home Hub allows it to be updated when BT "push" new releases out. This has happened twice whilst I have had mine, and the first update (I assume by error) resulted in the pre-assigned IP addresses of my internal network becoming lost. The second upgrade some months later went fine and I only found out about it when I next logged in as router administrator and found a revised navigation layout.
*As with most routers it is possible to "re flash" a BT Home Hub (actually a rebadged and "ipodesque style" reboxed Thomson unit) to run different software. Pages of info exist on the web about how to do this and what the effects are.